I'm what you'd call a "super casual" twitter user. That is to say, I don't really use it other than for occasional real-time updates on things (After the NYC-area earthquake last year, Twitter was the first place I went to see what was up. And during the debates this year, I had fun following along with #debate.)
I can't be alone. And in those (rather specific, yes I know) cases, there is some opportunity for advertising, because just like when I use Google, I was searching for something, and to the OPs point, more open to buying that umbrella.
(For example, if a fact-checking group like PoliFact were advertising for me to follow them during my #debate search and "get real-time fact-checking", that's something I'd have totally subscribed to. Meanwhile I found them through sorting through the tweets instead.)
So I suppose it boils down to the same thing as with Google -- I don't really want to see ads when I'm reading Gmail, but I certainly don't mind them when I'm searching. Twitter could focus on promoted tweets / accounts during searches and I don't think they'd have the umbrella-in-a-synagogue problem.